Learning through Simultaneous Play: Evidence from Penny Auctions

This paper contributes to the emerging empirical literature on penny auctions, a particular type of all‐pay auctions. We focus on the potential learning effects that bidders may experience over time but also (and particularly) across auctions as a result of their auction participation. Using detailed bid‐level information, we find that, similarly to earlier literature, bidders suffer from a sunk cost fallacy, whereby their probability of dropping out of an auction is decreasing in the number of bids they have already placed in that auction. Although we do find that learning through repeated participation alleviates the sunk cost fallacy, participation in simultaneous penny auctions emerges as a much more effective learning mechanism, ultimately contributing toward bidders earning higher individual surpluses.     

Asymmetry in first‐price auctions with affiliated private values

Collusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two‐step non‐parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Revenue equivalence and income taxation

This paper considers the classical independent private values model of auction theory in the presence of income taxation. We show that revenue equivalence remains valid if income taxes are proportional. Progressive and regressive taxes lead, in general, to asymmetries between bidders with the well-known consequence that revenue equivalence no longer holds. However, if symmetry of the bidders is maintained, progressive (regressive) income tax implies a higher (lower) expected revenue in first-price than in second-price auctions. Financial support by theDeutsche Forschungsgemeinschaft is gratefully acknowledge.     

Anticipation of Auction Fever: Entry Decision,Reserve Price and the Choice of Auction Design

This paper analyzes the entry decision of rational bidders who expect to experience auction fever in English auctions. It shows that nonparticipation decision reduces seller's expected profit and this effect may outweigh the positive effect of the auction fever. We analyze the choice between English and second‐price sealed‐bid auctions and the optimal reserve price in English auctions. We show that it might be optimal for the seller to set a reserve price below her own valuation of the object. Finally, we show that the order in which bidders place their bids matters and the first bidder always has an advantage. Copyright © 2011 John Wiley & Sons, Ltd.     

Almost Common Value Auctions: An Experiment

In almost common value auctions one bidder has a higher (private) value for the item than the other bidders. Theory predicts that even a small private value advantage can have an explosive effect in English auctions, with advantaged bidders always winning and sharp decreases in revenue. These predictions fail to materialize for experienced bidders who have learned to avoid the worst effects of the winner's curse. Bidding is better characterized as proportional, with advantaged bidders tending to bid as in a pure common value auction after adding their private value advantage to their estimated value of the item.     

Second-Price Auctions with Asymmetric Payoffs: An Experimental Investigation

A series of two-player, second-price common-value auctions are reported. In symmetric auctions, bidders suffer from a winner's curse. In asymmetric auctions in which one bidder has a private value advantage, the effect on bids and prices is proportional rather than explosive (the prediction of Nash equilibrium bidding theory). Although advantaged bidders are close to making best responses to disadvantaged bidders, the latter bid much more aggressively than in equilibrium, thereby earning negative average profits. Experienced bidders consistently bid closer to the Nash equilibrium than inexperienced bidders, although these adjustments towards equilibrium are small and at times uneven.     

The impact of reserve prices on the perceived bias of expert appraisals of fine art

We examine whether expert appraisals provided to bidders before major art auctions are unbiased indicators of value. Despite a strong grounding in theory, this aspect of optimal auction design has been frequently challenged in previous empirical research, particularly in the market for fine art. We adopt a valuation benchmark that incorporates sellers' reserve prices as well as high bids, and recognize censoring of works that fail to make reserve. Although the auction houses never divulge reserve prices, we exploit the fact that they can be observed indirectly via their impact on buy‐in rates. Using the set of French Impressionist paintings brought to auction from 1985 to 2001, we estimate the distribution of reserve prices, establish their link to a proper valuation benchmark, and isolate the selection bias due to bought‐in works on the perceived market value of fine art works. After controlling for the impact of reserve prices, and considering all works brought to auction, we find no evidence of bias in the experts' pre‐sale estimates. Copyright © 2010 John Wiley & Sons, Ltd.     

An empirical model of the multi‐unit,sequential, clock auction

We construct a model of participation and bidding at multi‐unit, sequential, clock auctions when bidders have multi‐unit demand. We describe conditions sufficient to characterize a symmetric, perfect‐Bayesian equilibrium and then demonstrate that this equilibrium induces an efficient allocation. We propose an algorithm, based on the generalized Vickrey auction, to calculate the expected winning bid for each unit sold. This algorithm allows us to construct a simulation‐based estimator of the parameters for both the participation process and the distribution of latent valuations. We apply our method to data from 37 multi‐lot, sequential, English auctions of export permits for timber held in Russia. Copyright © 2006 John Wiley & Sons, Ltd.     

Econometric models of asymmetric ascending auctions

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that conditions for the existence and uniqueness of an increasing-strategy equilibrium are essentially identical to those which ensure a unique and increasing solution to the system of equations. We exploit the computational tractability of this characterization in order to develop an econometric model, thus extending the literature on structural estimation of auction models. Finally, an empirical example illustrates how equilibrium learning affects bidding during the course of the auction.     

Preference for bid time in hybrid auctioned IPOs: Evidence from China

Using comprehensive bidding data of 783 Chinese IPOs from June 2009 to November 2012, we investigate institutions’ preference for bid time in hybrid auctions. We find that (1) earlier bids are associated with higher pricing errors, which is more pronounced in IPOs with greater uncertainty; (2) the bid prices of earlier bids tend to be aggressively high; (3) earlier bids are associated with fewer bid shares and allocations; (4) bidders submitting earlier bids (hereafter, earlier bidders) have inferior profits; and (5) earlier bidders show persistence in bid time. Overall, the empirical results remain robust after controlling for unobserved bidder-underwriter relationships and indicate that earlier bidders tend to be less informed. Our findings reveal and highlight the effect of bid time on identifying informative bids in hybrid auctions.     

Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999     

Bundling and the Reduction of the Winner's Curse

The paper studies the effects of bundling on the bidding strategies and seller revenues in auctions when the bidders have common values for the objects. Bundling of objects before the auction reduces the problem of the winner's curse, and the bidders bid more aggressively. This does not mean that a bundled auction is always better for the seller's revenue. Indeed, there is another effect that makes the bundled auction preferable (from the seller's standpoint) if and only if the number of bidders is small. While this is the only effect present in an independent-private-values model, it does not vanish when bidders have pure common values for the objects. The paper concludes that a bundled auction is unambiguously better for the seller than separate auctions when the number of bidders is small.     

Corners in Auctions

Different pricing rules in multiunit auctions provide different incentives for a bidder to corner the auction and thus require different levels of effort from the seller to deter cornering. We consider three different types of auctions: the pay-your-bid or "discriminatory" auction commonly used by the US Treasury, the lowest-winning-bid uniform-price auction used in the current Treasury experiment, and the highest-losing-bid uniform-price auction considered by Vickrey almost four decades ago. We show that the pay-your-bid auction provides the greatest incentive to corner the market, that the experimental Treasury auction provides less incentive, and that the highest-losing-bid uniform-price auction provides the least. Arguably, the less the incentive to corner the market, the easier it will be for sellers to deter cornering, and the greater their expected revenue (net of the cost to deter cornering) will be in otherwise expected-revenue-equivalent auctions.     

Posterior odds comparison of a symmetric low-price,sealed-bid auction within the common-value and the independent-private-values paradigms

I attempt to decide, using the posterior odds ratio, whether the symmetric common-value paradigm or the symmetric independent-private-values paradigm is a more probable explanation of the low-price, sealed-bid auctions conducted by the Indian Oil Corporation to purchase crude-oil from the international market. The estimation approach is structural parametric. The auctions are modelled as static non-cooperative games of incomplete information with risk neutral bidders. I conclude that the symmetric independent-private-values paradigm is more probable. Copyright © 1999 John Wiley & Sons, Ltd.     

The FCC Spectrum Auctions: An Early Assessment

This paper analyzes six spectrum auctions conducted by the Federal Communications Commission from July 1994 to May 1996. These auctions were simultaneous multiple-round auctions in which collections of licenses were auctioned simultaneously. This auction form proved remarkably successful. Similar items sold for similar prices, and bidders successfully formed efficient aggregations of licenses. Bidding behavior differed substantially in the auctions. The extent of bidder competition and price uncertainty played an important role in determining behavior. Bidding credits and installment payments also played a major role in several of the auctions.     

Information Precision and Common Value Partnership Dissolution: An Experimental Study

This paper develops a simple model of ½ auctions in a partnership dissolution game with common values, analyzes how information precision affects the equilibrium, and uses a laboratory study to test the model's predictions. Consistent with the model's prediction, the study shows that when bidders have the same quality information, higher precision leads to more extreme bids. In the case of unequal precision, bidders must use the same bidding functions regardless of their own information quality, and thus, the equilibrium strategy should be the same for both bidders. The experimental results, however, contradicts this prediction. Copyright © 2016 John Wiley & Sons, Ltd.     

Preemptive bidding in takeover auctions with affiliated values

This paper extends Fishman's (1988) model of preemptive bidding in takeover auctions to auctions with affiliated values. It shows that preemptive bidding transfers wealth from the seller to the first bidder without affecting the profit of the second bidder and social welfare. It also shows that higher correlation between bidders’ values leads to higher preemption rates but has an ambiguous effect on the size of the opening bid. Finally, it shows that in auctions with affiliated values, even infinitesimal entry costs may lead to a preemptive jump bidding that allows the reallocation of the entire surplus from the seller to the first bidder.     

Bayesian estimation approaches to first-price auctions

This paper considers Bayesian estimation strategies for first-price auctions within the independent private value paradigm. We develop an ‘optimization’ error approach that allows for estimation of values assuming that observed bids differ from optimal bids. We further augment this approach by allowing systematic over or underbidding by bidders using ideas from the stochastic frontier literature. We perform a simulation study to showcase the appeal of the method and apply the techniques to timber auction data collected in British Columbia. Our results suggest that significant underbidding is present in the timber auctions.     

Econometrics of first-price auctions with entry and binding reservation prices

This paper considers the structural analysis of first-price auctions with entry and binding reservation prices. The presence of entry decisions and binding reservation prices complicates the structural analysis. Building on the recent theoretical work on entry in auctions, this paper assumes that each potential bidder first decides whether or not to incur an entry cost and become an active bidder using a symmetric mixed strategy. Then each active bidder bids optimally following the increasing Nash–Bayesian equilibrium strategy. Using the observed bids and the number of actual bidders, we propose an MSM estimator to estimate the parameters in the distribution of private values and the distribution of the number of active bidders. Our approach can be used to validate the theoretical auction model, to test whether the reservation prices are binding, and to test the mixed-strategy of entry.